Most prepositions take the accusative, I think, the most obvious exceptions being those that indicate motion away (ab, ex, dē), "cum", "sine", "prō", and some uses of "in". There are others, but those are the most common ones that take the ablative.

One thing that's strange is that "ante" takes the accusative and "prae" takes the ablative, even though as far as I can tell, they're synonymous.

EDIT: I just found a mnemonic for which prepositions can take the ablative: SID SPACE.SubInDē

SinePrōAbCumEx

This does leave out a couple ("prae" is probably the most significant), but it's close.